Vrije Universiteit Brussel. Faculteit Wetenschappen Departement Natuurkunde

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1 Vrije Universiteit Brussel Faculteit Wetenschappen Departement Natuurkunde Measurement of the top quark pair production cross section at the LHC with the CMS experiment Michael Maes Promotor Prof. Dr. Jorgen D Hondt Proefschrift ingediend met het oog op het behalen van de academische graad Doctor in de Wetenschappen September 23

2 Doctoral examination commission Chair: Prof. Dr. N. Van Eijndhoven (VUB) Supervisor: Prof. Dr. J. D Hondt (VUB) Secretary: Prof. Dr. F. Blekman (VUB) Prof. Dr. S. Bentvelsen (NIKHEF) Prof. Dr. S. Lowette (VUB) Prof. Dr. A. Sevrin (VUB) Prof. Dr. R. Tenchini (INFN/Pisa) Prof. Dr. ir. G. Vandersteen (VUB)

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5 Contents Introduction The top quark sector of the Standard Model 3. The Standard Model Fermions and bosons: the building blocks of the universe The Standard Model as a quantum field theory Spontaneous symmetry breaking: generating particle masses Extensions of the Standard Model The heaviest quark, the top quark Production and decay Other top quark properties Implications for the Standard Model The top quark as a calibration tool The Large Hadron Collider and the CMS experiment 7 2. The Large Hadron Collider Design of the collider The experiments at the LHC The LHC run periods The Compact Muon Solenoid experiment Overview of the detector systems The CMS coordinate system The tracking detector The calorimeters The muon system The trigger system The LHC computing grid CMS Data taking during the 2 and 22 LHC runs Simulation and reconstruction of proton-proton collisions Event generation chain The hard interaction Parton showering Matching Parton Showers and Matrix Elements Hadronization Decay v

6 vi CONTENTS 3..6 Underlying event Overview of the generated event samples Comparison of different t t generators Detector simulation Object reconstruction Pileup interactions The ParticleFlow Algorithm Muon reconstruction and identification Electron reconstruction and identification Additional electron identification Hadron and photon reconstruction Jet reconstruction Missing Transverse Energy reconstruction ( E/ T ) Bottom quark identification Track impact parameter significance based algorithms Secondary vertex based algorithms Soft lepton based algorithms Combined secondary vertex algorithm b-tagging performance Event selection Selection of l+jets t t events Online trigger Primary vertex selection Lepton selection criteria Jet selection criteria E/ T selection criteria Event selection results Reweighting for soft p top T spectrum in simulation Topology reconstruction Associating jets to partons with a χ 2 -based jet matching Jet matching performance Measurement of the b tagging efficiency Constructing the b jet candidate sample Reconstructing the b-tag discriminator distribution Data-driven estimation of the scale factor F Constructing a non b jet control sample Reweighing the control sample kinematics Studying the bias of the method Correlation of b with M lj Effect of the χ 2 min cut Correlation of light jets b with M lj for CSV taggers Data-driven estimation of the inclusive b-tagging efficiency Statistical properties of ˆɛ b Systematic uncertainties

7 CONTENTS vii 5.8 Results at s = 8 TeV Track Counting High Efficiency (TCHE) Combined Secondary Vertex (CSV) Results at s = 7 TeV Track Counting High Efficiency (TCHE) Combined Secondary Vertex (CSV) Summary Measurement of the mis-tagging efficiency 4 6. Reconstructing the non-b jet b-tag discriminator distribution Estimation of the total mis-tagging efficiency Correlation between ˆɛ b/ and ˆɛ b Parton flavour composition of the signal sample Statistical properties of ˆɛ b/ Systematic uncertainties Results for the different b-tagging algorithms Track Counting High Efficiency (8 TeV) Combined Secondary Vertex (8 TeV) Track Counting High Efficiency (7 TeV) Combined Secondary Vertex (7 TeV) Summary Measurement of the t t production cross section Estimating the number of top quark pairs in data Determining the total event selection efficiency Theoretical acceptance (A) Event selection efficiency at reconstruction level (ɛ sel ) Jet-lepton mass overflow bin removal (ɛ Mlb ) Jet combination threshold (ɛ χ 2) Efficiency of the b-tagging cut (ɛ btag ) Results in the electron and muon channels Statistical properties of σ t t Systematic uncertainties Constraining the Jet Energy Scale uncertainty Performing the l+jets combination The BLUE method Results for the σ t t combination Cross section ratio between different LHC beam energies Summary of the results Results at 7 TeV Results at 8 TeV /7T ev Results for Rσ t t Results for other b-tagging algorithms

8 viii CONTENTS 8 Conclusions and Perspectives Measurement of the b-tagging performance Measurement of the inclusive t t cross section Measurement of the 8 to 7 TeV t t cross section ratio Bibliography 25 Summary 25 Samenvatting 27 Acknowledgements 22

9 Introduction All the particles that constitute the matter of the universe and the forces governing them, except gravity, are described by a theory called the Standard Model. This theory has been formulated in the 97s and since then has been validated in numerous experiments. To date, the predictions made by this theory have been validated to high precision which is the basis of its success. However, the Standard Model has its flaws such as the inability to describe gravity. One of its longstanding issues was the inability to incorporate the mass of massive particles. This was solved by Brout, Englert and Higgs introducing a new mechanism to attribute mass to particles. For this method to be validated, a boson called the Brout-Englert-Higgs boson has to be discovered. To search for new phenomena as well as the illusive BEH boson, large particle colliders have to be built where the universe can be probed at it s smallest scales. The Large Hadron Collider (LHC) that has been constructed at CERN came into operation in March 2 and is the largest and most energetic collider in the world colliding proton beams at 7 and 8 TeV. To study these proton-proton collisions provided by the LHC, large experiments have been constructed and among them is the Compact Muon Solenoid (CMS). The latest success of the Standard Model came when in 22 the CMS and ATLAS collaborations claimed the discovery of a boson that is consistent with the long-sought Brout-Englert-Higgs boson. Nevertheless, the search for new phenomena continues at full force. The top quark, the heaviest particle in the Standard Model, plays a very important role in the research at the LHC. The large sample of top quark events produced at the LHC provides a unique opportunity to measure this quarks properties with great precision. The production cross section of top quark pairs, for example, does not only benchmark the perturbative calculations in QCD but is also sensitive to various hypothetical new physics phenomena that would modify its value. Additionally, the top quark also serves as a calibration tool. Since it almost exclusively decays into a W boson and a b quark, the large sample of b quarks can be used to calibrate b quark identification, or b-tagging, algorithms. These algorithms are used by various analyses to isolate signal processes containing b quarks in the final state from the usually abundant backgrounds. In this thesis, a fully data-driven method is introduced to measure the b-tagging efficiency as well as its mis-tagging efficiency. Furthermore, b-tagging is used to isolate the top quarks from the background to measure the top quark pair production cross section. In Chapter, the Standard model is introduced along with the current status of the

10 2 INTRODUCTION top quark research. Subsequently, the Large Hadron Collider and the CMS experiment are introduced in Chapter 2. To be able to develop and benchmark analysis techniques, simulated events are required. The event generation and detector simulation procedure is outlined in Chapter 3 together with the reconstruction of the detector signals to physics objects. Then, the reconstructed events can be passed along to the event selection step in Chapter 4 to separate signal and background events. In Chapter 5 the method to measure the b-tagging efficiency is introduced. This method is then extended in Chapter 6 to also measure the mis-tagging efficiency. The measurement of the top quark pair cross section is then detailed in Chapter 7. Finally, Chapter 8 concludes on the measurements and provides some future perspectives. The results presented in Chapters 5, 6 and 7 are based on my own research. The measurement of the b-tagging efficiency has been published in [ 3] and the t t cross section in [4 6] with a paper publication for the 8 TeV result still in the pipeline. Finally, the measurement of the mis-tagging efficiency has not been made public so far.

11 Chapter The top quark sector of the Standard Model In our universe, all matter is built up by tiny invisible particles. These elementary particles interact according to fundamental forces. Consequently, a theory describing the dynamics of our universe is required to contain a consistent description of all these particles and how they interact. The Standard Model of Particle Physics, or Standard Model (SM), effectively describes the known particles in our universe and is able to incorporate three out of four fundamental forces. Moreover, the Standard Model does not only excel in being the best attempt at a unified theory of the universe; it also excels in the high precision by which it can predict the outcome of numerous experiments carried out since its birth during the second part of the 2 th century. One particle of the Standard Model is of particular interest in current research, namely the top quark. This quark was discovered in 995 and to date is the heaviest known elementary particle. Its importance in the understanding of the Standard Model and the universe is two-fold. First, this quark provides a unique window to phenomena beyond the reach of the Standard Model as new hypothetical particle can decay in top quarks. Secondly, the top quark can be used as an experimental calibration tool to further improve precision measurements.. The Standard Model The fundamental particles building up all matter in the universe are described by the Standard Model along with the electromagnetic, weak and strong forces that govern them [7 9]. Each of these three forces is accompanied by a force-carrying particle. In the first Section, the matter particles or fermions are introduced along with the force-carrying particles called bosons. Subsequently, in Section..2, these particles will be described as fields in a quantum field theory. In this framework, the fields can interact among each other by requiring the theory to be invariant under local gauge transformations. Furthermore, the gauge groups that make up the Standard Model will be discussed. Additionally, the mechanism of spontaneous symmetry breaking that An elementary particle cannot be further decomposed in other even smaller particles. 3

12 4 CHAPTER : The top quark sector of the Standard Model gives mass to all particles will be introduced. To end the discussion on the Standard Model, some of its problems and possible extensions will be outlined in Section Fermions and bosons: the building blocks of the universe In the Standard Model two main categories of particles are distinguished: the bosons and the fermions. The twelve fermions, or matter particles, are considered to built up all known matter. Secondly the bosons, or force-carriers, are associated to the forces that govern the interaction between the particles. The fermion group consists of 2 half-integer spin particles that are either labeled a lepton or a quark. The leptons group consists of the electron (e ), muon (µ ) and the tau (τ ) particles. For each of these leptons an associated neutrino exists. These particles are charge neutral and as a consequence can only interact through the weak force. Because of their negligible mass (<< ev ), neutrinos are considered massless throughout this thesis. Conversely, since the leptons carry a negative electrical charge they can interact both through the weak and the electromagnetic forces. The negative elementary charge of - e for the leptons is further emphasised by the minus superscript in their symbol. The second group of fermions consists of quarks. Each fermion generation distinguishes an up-type and a down-type quark. The up-type quark carries a +2/3 e charge while the down-quark has a /3 e electrical charge. As opposed to the leptons the quarks can also interact through the third fundamental force described by the Standard Model being the strong interaction. Each of the fermions has an anti-particle with the same mass but an opposite electrical charge. The anti-particle of fermion f is denoted as f. For the charged leptons, the anti-lepton is denoted with a + superscript rather than putting a bar on the symbol. This clearly states that the anti-lepton has a positive charge. Moreover, the anti-electron is called a positron. Generation Generation 2 Generation 3 Electrical charge Leptons e (electron) µ (muon) τ (tau) e ν e (electron neutrino) ν µ (muon neutrino) ν τ (tau neutrino) Quarks u (up) c (charm) t (top) +2/3 e d (down) s (strange) b (bottom) /3 e Table.: Overview of the fermions in the Standard Model along with their electrical charge Within the fermion group, three generations can be identified as shown in Table. where each generation consists of a lepton, an associated neutrino and two quarks. The first generation is considered to built up all visible matter in the universe while all subsequent generations contain particles with identical quantum mechanical properties except for a higher mass. The proton consists of two up quarks and one down quark while a neutron is composed of two down quarks and one up quark. Protons and

13 CHAPTER : The top quark sector of the Standard Model 5 Boson Mass (GeV) Electromagnetic force Photon (γ) Massless Weak force W ± ±.5 Weak force Z ±.2 Strong force 8 gluons (g) Massless Generating mass H 25.7 ±.4 Table.2: Bosons of the Standard Model [, ] neutrons along with electrons in their turn build up atoms which build up all known matter. The second and third generation do not occur as stable particles in nature, nevertheless they are present in cosmic rays and can be produced under laboratory conditions as well. The forces that allow the fermions to interact are carried by integer-spin particles called bosons. First the electromagnetic force is governed by the massless photon. Next the massive W ± and Z bosons carry the weak interaction. Finally, the strong force is accompanied by eight massless gluons. These particles are summarised in Table.2 together with their masses. In this table, the quoted unit of mass is GeV rather than GeV/c 2 since in this thesis the convention c= is used. In addition to the bosons carrying the three fundamental forces incorporated within the Standard Model there exists one more spin-zero boson: the Brout-Englert-Higgs (BEH) boson. This boson gives mass to all other particles via the mechanism that will be explained in Section..3. This boson was only recently discovered in 22 by both the CMS and ATLAS experiments at the Large Hadron Collider [2, 3]...2 The Standard Model as a quantum field theory To lay out the theoretical foundation of the Standard Model, quantum field theory is used. The virtue of this framework is that it combines both quantum mechanics and special relativity. In this theory, the fermions are described by fields and the interactions between the fields come around by demanding the theory to be gauge invariant. First it will be shown how the Lagrangian density for such theory could be obtained. Afterwards the gauge groups constituting the Standard Model will be explained. Interacting fields through local gauge invariance In the Standard Model, fermions are represented by fields, more precisely Dirac-spinor fields ψ. The Lagrangian for this theory is thus the Dirac Lagrangian which can be written in terms of the fermion field ψ, the anti-fermion field ψ, the particle mass m and the Dirac γ-matrices. L Dirac = i ψγ µ µ ψ m ψψ (.)

14 6 CHAPTER : The top quark sector of the Standard Model To obtain a gauge invariant theory, invariance of the Dirac Lagrangian under a local phase transformation is enforced. This local phase transformation is given by ψ = Uψ = e iɛa (x) τa 2 ψ (.2) where ɛ a (x) (a=,...,n) are parameters for a n-dimensional Lie-group with generators τ a. To make the Dirac Lagrangian invariant under this transformation, the normal derivative µ is to be replaced by a so-called covariant derivative defined as D µ = µ ig τ a 2 Aa µ (.3) The covariant derivative ensures the invariance of the Lagrangian under this local gauge transformations and introduces new interacting fields A a µ. The Dirac Lagrangian now becomes L = i ψγ µ D µ ψ m ψψ = i ψγ µ µ ψ m ψψ + g ψγ µ τ a 2 Aa µψ. (.4) where the last term in the Lagrangian shows the interaction between the fermion fields and the new vector fields. The factor g is called a coupling constant and is proportional to the interaction strength. The technique of requiring the theory to be invariant under local gauge transformations, or so-called local gauge symmetry, has shown to yield interacting fields in the Lagrangian. When representing the gauge transformation in an Abelian group including commuting generators, the resulting interacting fields can only couple to the fermion fields. Conversely, if the transformation is represented by a non-abelian group, the gauge fields can also couple among themselves. Gauge groups of the Standard Model As mentioned at the beginning of this chapter the Standard Model incorporates three of the fundamental forces in nature. As a consequence, three gauge groups are defined as G SM = SU(3) C SU(2) L U() Y (.5) where the first group represents the gauge symmetry of the strong force and the other two the gauge symmetry of the unified electroweak force. To describe the electroweak interaction the Lagrangian has to be gauge invariant under SU(2) L U() Y. This can be achieved by introducing the following covariant derivative D µ = µ ig τ a 2 W a µ ig Y 2 B µ (.6) The factors g and g are the respective coupling constants, τ a are Pauli matrices and the hyper charge is denoted as Y. The local gauge invariance under the Abelian group U() Y introduces a field B µ. Moreover, the local gauge invariance under SU(2) L introduces three gauge fields W a µ, a={,2,3}. These fields do however not immediately

15 CHAPTER : The top quark sector of the Standard Model 7 represent the bosons discussed in the first section. To obtain these bosons, linear combinations of the gauge fields have to be taken to generate them. Consequently, the W boson is defined as ( ) W µ ± = W 2 µ iwµ 2. (.7) The neutral Z boson is defined as Z µ = W 3 µ cos θ w B µ sin θ w. (.8) And finally, the photon can be obtained using the following linear combination A µ = W 3 µ sin θ w + B µ cos θ w. (.9) In the previous equations, the Weinberg angle (θ w ) is defined as tan θ w = g g. (.) The strong interaction is described in terms of quantum chromodynamics (QCD). Requiring the Lagrangian to be invariant under the transformations of the non-abelian SU(3) C group generates an additional eight gauge fields G a µ, a=,...,8. These gauge fields represent the eight gluons introduced in this chapter. To obtain the local gauge symmetry again a covariant derivative is defined as D µ = µ ig s λ a 2 Ga µ, (.) where λ a are the Gell-Mann matrices and g s is the strong coupling constant. The subscript C in the group definition emphasises the fact that quarks that transform as a triplet under SU(3) C carry a colour charge and gluons are coloured as wel. The eight gluons can also interact among themselves as the group is non-abelian. To accommodate, amongst others, the experimental observation of CP violating processes, the quark eigenstates in the strong interactions are considered to differ slightly from these in the weak interaction. Hence a matrix is defined linking the quark eigenstates from both the strong and weak interactions, also known as the Cabibbo- Kobayashi-Maskawa (CKM) matrix. This matrix is defined as d weak V ud V us V ub d s weak b weak = V cd V td V cs V ts V cb V tb s b (.2) L where each element V ij is proportional to the probability of quark type i to dacay into a quark from type j through the charged weak interaction...3 Spontaneous symmetry breaking: generating particle masses In Section.. the force-carrying particles were introduced. The photons and gluons, governing the electromagnetic and strong forces respectively, are massless. In contrast to the massless bosons, the weak interactions W ± and Z bosons are massive. L

16 8 CHAPTER : The top quark sector of the Standard Model Although the electroweak interaction is unified in the Standard Model the symmetry should be broken at low energies. To generate mass for the W ± and Z bosons, a mass term can be added to the Lagrangian. As a consequence the invariance under local gauge transformations is broken which breaks the gauge symmetries of the Standard Model. Hence, the implementation of these explicit mass terms is forbidden. Another strategy to add mass to particles is through the mechanism of spontaneous symmetry breaking [4] often called the Brout-Englert-Higgs (BEH) mechanism [5, 6]. The easiest way to break the electroweak gauge symmetry is to add a scalar SU(2) field φ ( ) φ + φ =, (.3) to the Lagrangian. This ensures the invariance under local gauge transformations while breaking the gauge symmetry of the vacuum. The fields φ + and φ are complex fields. This provides the following Lagrangian: φ L Brout Englert Higgs = (D µ φ) D µ φ V (φ) (.4) = (D µ φ) D µ φ µ 2 ( φ φ ) λ ( φ φ ) 2, (.5) where λ is a positive number representing the strength of the field self interaction. The mass parameter µ 2 defines two possible scenarios. For µ 2 >, the potential V (φ) reaches a minimum at φ =. Additionally, for µ 2 < the minimum is no longer unique and the potential now reaches a minimum when φ 2 = φ φ = µ2 2λ = v2 2. (.6) The vacuum can now be written as a quantum fluctuation around the vacuum expectation value v φ = ( ), (.7) 2 v + h(x) where the only real field is h(x). This field is called the Brout-Englert-Higgs boson field. This field is associated with a scalar boson, called the Brout-Englert-Higgs boson, with a mass M H = 2λv 2. For the vacuum to be stable, λ has to be positive at all scales Q, this introduces a lower bound for M H. The remaining three complex fields are absorbed by the W ± and Z bosons to acquire their mass. Inserting the covariant derivative from the electroweak theory into the Lagrangian in Eq..5 leads to the mass terms for the electroweak gauge bosons. m W = 2 v g m Z = 2 v g 2 + g 2 (.8) The fermions do not acquire mass in the same way as the bosons. Here a Yukawa coupling term is added to the Lagrangian depicting the coupling of the fermion fields to the Brout-Englert-Higgs field. These gauge invariant interaction terms are defined as L Y ukawa = g Y ukawa φ ψψ, (.9)

17 CHAPTER : The top quark sector of the Standard Model 9 where g Y ukawa is the coupling constant and the fermion mass equals m fermion = g Y ukawa v/ 2. (.2) Until the summer of 22, this mechanism was believed to be responsible for generating particle masses yet no experimental evidence was at hand. Hence, the discovery of a new spin- boson by the CMS and ATLAS collaborations at the Large Hadron collider [2, 3] compatible with the Brout-Englert-Higgs boson is one of the major breakthroughs in the understanding of the Standard Model...4 Extensions of the Standard Model The Standard Model is by far one of the most tested theories in physics to date. Numerous precision measurements have been carried out to test its validity and so far everything agrees well. With the discovery of a scalar BEH-like boson in 22, the foundation of the Standard Model became even stronger as now it is able to describe how particles get their mass. In contrast to its successes, the Standard Model has some theoretical and experimental shortcomings. A few of them will be discussed in the following. Unification of all forces: Although the electric and magnetic forces are unified in the theory of electromagnetism which in its turn is mixed with the weak force in the electroweak interaction, there exists no unification of the strong force with the latter. There is no strong argument from theory to have such unified theory, nevertheless it is expected that at some very large energy scale the forces are indeed unified and this unification breaks spontaneously at the energy scales where the forces appear to be distinct. No description of gravity: Apart from the lack of a complete unification of the three fundamental forces in the Standard Model, it can also not describe the gravitational force. This is one of the main issues since this prevents the Standard Model from becoming the unified theory explaining all phenomena in the universe. The hierarchy problem: One of the open problems in the Standard Model is the hierarchy problem. This problem relates to the large discrepancy between the electroweak energy scale, on the order of 2 GeV, and the Planck scale around 9 GeV where gravity starts playing a crucial role. In this large gap between the two energy scales no new phenomena are predicted. Therefore the relatively light mass of the BEH boson induces very large corrections on the parameters of the Standard Model. Most of our universe is unknown: Only a small fraction of all matter in the universe is known and incorporated in the Standard Model. Recent observations from the Planck satellite [7] have shown that the known matter constitutes 4.9% of the universe while 26.8% is considered to be dark matter and the remainder 68.3% dark energy. Neither of the last two can be described by the Standard Model.

18 CHAPTER : The top quark sector of the Standard Model The above mentioned problems do not, however, suggest that the Standard Model is wrong or should be overruled. Given its experimental success and the level of precision achieved when making predictions it is considered to be incomplete. One of the possible extension theories of the Standard Model is SuperSymmetry [8]. This theory predicts the existence of super partners for each currently existing particle that are identical in any way except that the particle and its super partner differ in spin by /2. This entails that the super partner of a boson is a fermion and vice versa. The benefit of this extension is that it allows for a unification of the strong and electroweak forces and it incorporates a potential candidate to constitute dark matter: the neutralino. Moreover, due to the existence of a new range of super particles, the radiative corrections to the BEH boson mass can become smaller essentially solving the hierarchy problem. To test models like SuperSymmetry, particle colliders like the Tevatron collider at Fermilab and the Large Hadron Collider at CERN are constructed to continuously probe higher and higher energy scales. These experiments along with numerous noncollider experiments, such as neutrino factories, hope to unravel the mysteries of the Standard Model..2 The heaviest quark, the top quark Among all particles in the Standard Model, the top quark is by far the most massive with a current world average mass of 73.2±.87 GeV [9]. To produce a heavy quark like the top quark, a hadron collider needs to reach a multi-tev centre-of-mass energy. The first collider that was able to produce them is the Tevatron p p collider located at Fermilab nearby Chicago. At this collider, the top quark was discovered in 995 by the CDF [2] and DØ [2] collaborations more than 2 years after the discovery of the bottom quark. Hence, the Large Hadron Collider at CERN is the second machine that can produce this heavy quark and the first that will do so in large numbers. This opens a wide area of top quark research at the LHC. In Section.2., the production and decay characteristics of the top quark will be discussed. Furthermore, the state-of-the art measurements of the top quark mass and other key properties are outlined in Section.2.2. The implications for the Standard Model are discussed in Section.2.3 and the potential of using the top quarks as a calibration tool is discussed in Section Production and decay Top quarks can be produced in proton-proton collisions at the LHC in two ways. First, the top quark can be produced through the electroweak interaction as a single top quark or anti-top quark. Secondly, the top quark can be produced in pairs of top and anti-top quarks through the strong interaction. The latter is the more dominant production mechanism and is the main focus of this thesis. The single-top production will not be further discussed. In the proton-proton collisions delivered by the LHC, top quark pairs can be formed by an annihilation of two quarks, q q t t or by fusion of two gluons, gg t t. At the LHC, gluon fusion is the dominant mechanism for producing top-quark pairs.

19 CHAPTER : The top quark sector of the Standard Model One of the important characteristics of the t t production mechanism is the cross section. This is the effective area that governs the probability of an absorption or scattering event. In terms of particle physics, this observable is interpreted as the likelihood of a certain interaction between particles. The top quark pair cross section is known theoretically as complete next-to-next-to-leading order calculations are available [22, 23] with next-to-next-to-leading log corrections applied. This means that the cross section is theoretically known up to O(αs) 4 with a precision of % at s = 7 TeV and % at 8 TeV. The precise measurement of the t t pair production cross section is important for two main reasons. First, this measurement provides a crucial benchmark for the QCD perturbative calculations. Secondly, the t t pair production process could be enhanced or suppressed by new physics processes producing top quark pairs. Hence, the cross section could be sensitive to the presence of new phenomena. The t t pair production cross section has been measured both in p p collisions at the Tevatron collider and pp collisions at the LHC. Table.3 shows the latest result from the Tevatron ElectroWeak Working Group combining results from the CDF and DØ collaborations. The most precise results from the LHC are given as well. So far all measurements of this quantity agree well with the theoretical predictions. Collider s (TeV) σ obs t t (pb) σ NNLO+NNLL t t (pb) Tevatron.96 (p p) 7.65± Large Hadron Collider 7 (pp) 62.± Large Hadron Collider 8 (pp) 227. ± Table.3: Most precise measurements of the t t pair production cross section at the Tevatron [24] and at the LHC [25, 26] compared with the NNLO+NNLL theoretical calculations [22, 23]. The measurements assume a top quark mass of 72.5 GeV With a life time of the order of 25 s [3], about 2 times shorter than the typical timescale for the strong interaction, the top quark is the only quark in the Standard Model that can decay through the weak interaction. This makes the top quark very interesting to study as it is the only quark that can be directly accessed as a free quark in experiments. The top quark is expected to decay into a W boson and a lighter down-type quark. Hence, the top quark can either decay to a W boson with a d quark, an s quark or a b quark. The branching ratio of these three cases are governed by the matrix elements of the unitary CKM matrix introduced in eq..2. Measurements of the CKM matrix element V tb = (stat+sys) [3] show that V tb is consistent with and combined with the unitarity of the CKM matrix this results in the suppression of all decay modes except t W b. As a consequence, the decay of a t t pair is given as t t W + bw b. The W boson from the top-quark decay will decay in 2/3 of the cases into a pair of light quarks. Subsequently, in /3 of the cases the W boson decays into a charged

20 2 CHAPTER : The top quark sector of the Standard Model LHC, 4.8 s = 7 TeV LHC, 4.8 s = 8 TeV ATLAS e/ µ+jets 86 ± 3 ± 2 ± 7 pb L=2.5/fb (val. ± stat. ± syst. ± lumi.) ATLAS prel. (e/ µ+jets) 24 ± 2 ± 3 ± 9 pb L=5.8/fb (val. ± stat. ± syst. ± lumi.) ATLAS dilepton (ee, µµ,eµ) 76 ± 5 ± ± 8 pb 4 L=.7/fb (val. ± stat. ± syst. ± lumi.) L=2.8/fb (val. ± stat. ± syst. ± lumi.) CMS prel. (e/ µ+jets) 228 ± 9 ± ± pb CMS e/ µ+jets 58 ± 2 ± ± 4 pb L= /fb (val. ± stat. ± syst. ± lumi.) CMS prel. (ee, µµ,eµ) 227 ± 3 ± ± pb L=2.4/fb (val. ± stat. ± syst. ± lumi.) CMS dilepton (ee, µµ,eµ) 62 ± 2 ± 5 ± 4 pb CMS prel. combined 227 ± 3 ± ± pb (val. ± stat. ± syst. ± lumi.) L=2.3/fb (val. ± stat. ± syst. ± lumi.) NNLO+NNLL QCD, Czakon et al., arxiv: (23) NNLO+NNLL QCD, Czakon et al., arxiv: (23) σ(tt) (pb) Figure.: Measurement of the t t production cross section in the different decay channels at a centre-ofmass energy of 7 TeV [5, 25, 27, 28]. The measurements are compared to the full NNLO+NNLL theoretical calculation [22, 23] σ(tt) (pb) Figure.2: Measurement of the t t production cross section in the different decay channels at a centre-ofmass energy of 8 TeV [6, 26, 29]. The measurements are compared to the full NNLO+NNLL theoretical calculation [22, 23].

21 CHAPTER : The top quark sector of the Standard Model 3 lepton and its associated neutrino. Since the t t decay contains two bosons in the final state, it can decay in three different modes. When both W bosons decay into quarks or into a lepton and a neutrino, the decay mode is called fully hadronic and fully leptonic respectively. Conversely, when one of the two W bosons decays into a lepton and a neutrino while the other decays into quarks, the decay is called semi-leptonic. The latter, t t W + bw b q qblνl b, will be extensively studied in this thesis and accounts for 4.8% of all top quark pair decays per lepton flavour l. The t t production cross section has been measured in each of these decay channels. The most precise results from the CMS and ATLAS experiments at the LHC are provided in Figure. for s = 7 TeV and Figure.2 for s = 8 TeV. There exist some models where the top quark could decay differently. A search has been conducted for so-called Flavour Changing Neutral Current interaction (FCNC), i.e. a decay into a neutral Z boson and a quark. In the Standard Model such interaction is heavily suppressed so the observation of such interaction would hint new physics. However, the branching ratio of such process is found to be smaller than.2% at 95% C.L. [32]. Additionally, baryon number violating top quark decays were investigated [33]. Upper limits of.6% and.7% at 95% C.L. have been set on the branching ratios of t bcµ and t bue, respectively. Thus no deviation from the Standard Model prediction of the top quark decay characteristics have been found so far. Also the decay width (Γ) of the top quark is sensitive to new physics effects. As the top quark almost exclusively decays into a W boson and a b quark, its decay width is expected to be dominated by the partial t W b width, Γ(t W b). According to the Heisenberg uncertainty principle τ = /Γ, a decay width of.5 GeV for the top quark is predicted. The decay width is particularly interesting as it is very sensitive to new phenomena like anomalous Wtb couplings. A measurement carried out by DØ yields Γ t = GeV [3], consistent with expectations. Next to the total t t cross section measurement, it can also be measured as a function of different kinematic variables of the top quark decay products. Both the CMS and ATLAS experiments have carried out such measurements [34 37]. These measurements allow to further benchmark detailed theoretical predictions to the data collected by the respective experiments. Figure.3 is an example of the measurement of the t t cross section as a function of the mass of the t t system. Another example is provided in Figure.4 where the cross section is given as a function of the pseudo rapidity 2 of the leading lepton. These figures show in general a very good agreement between the data and simulation..2.2 Other top quark properties Next to the production and decay of top quarks, some other very interesting properties can be measured. One of these properties is the top quark mass. The mass has been 2 The pseudo rapidity of a particle is defined as η = ln [ tan ( θ 2)] where θ is the angle between the momentum vector of the particle and the beam axis.

22 4 CHAPTER : The top quark sector of the Standard Model GeV dσ tt dm σ -2-3 e/µ + Jets Combined CMS, 5. fb at s = 7 TeV Data MadGraph MC@NLO POWHEG NLO+NNLL (arxiv:3.5827) dσ dη Lead.l σ CMS Preliminary, 2.2 fb at Dilepton Combined s = 8 TeV Data MadGraph MC@NLO POWHEG m tt Figure.3: Differential t t cross section as a function of the mass of the t t system GeV η Lead.l Figure.4: Differential t t cross section as a function of pseudo-rapidity of the leading lepton measured at the Tevatron and at the Large Hadron Collider[9, 38 4]. Though the LHC produces larger top quark samples, the Tevatron still holds the most precise combined result of 73.2±.87 GeV [9]. The most precise measurement for each experiment is shown in Figure.5. The difference in mass between the top and anti-top quark has also been measured to great precision. This difference is sensitive to the CPT symmetry of the Standard Model that claims equal mass for a particle and its anti-particle. A mass difference of m t = 272 ± 96 ± 22 MeV was measured [4] which is compatible with zero. Due to the fact that the top quark has a shorter lifetime than the typical timescale of the strong interaction, it will decay and hence its spin information is transferred to its decay products. Hence the spin of the top and anti-top quarks can be reconstructed to check for correlation among them. This correlation is predicted by the Standard Model and has been observed at the LHC [42, 43]. The degree of correlation was found to be compatible to predictions. Next to that, the alignment of the top quark spin with its direction of movement, the top quark polarisation, has been measured as well [44, 45] and no deviation from the Standard Model has been observed. Another measurement has been carried out along these lines, the measurement of the W-boson helicity fractions from top quark pair decays. This measurement has been carried out to carefully study the W tb vertex and the helicity fractions were measured to be [46, 47] F =.626 ±.34(stat) ±.48(syst) F L =.359(stat).2 ±.28(syst), where F is fraction of longitudinal polarisation and F L is the fraction of left-handed polarisation. Using the requirement that all helicity fractions sum up to, the right-

23 CHAPTER : The top quark sector of the Standard Model 5 4 ATLAS lepton+jets 72.3 ±.75 ±.35 3 CMS lepton+jets ±.43 ±.98 2 CMS combination ±.38 ±.9 Tevatron combination March ±.5 ± (GeV) m t Figure.5: Most precise measurement of the top quark mass at the CMS [38] and ATLAS [39] experiments. The combination of the measurements of the DØ and CDF experiments at Tevatron is provided [9] as well as the combination of all mass measurements at CMS [4]. handed fraction F R can be inferred from the other two and equals.5±.34. These results are in good agreement with Standard Model predictions. Finally, the top quark charge has been measured. Since the top quark decays into a W boson and a b quark, its charge can either equal -4/3 or +2/3 of the elementary charge. The Standard Model predicts the top quark charge to be +2/3 and this is confirmed by measurement ruling out the -4/3 charge hypothesis at 95% C.L. [48, 49]..2.3 Implications for the Standard Model To check the consistency of the Standard Model to all available measurements, a global fit can be carried out. Since the discovery of a new boson at the LHC consistent with the Brout-Englert-Higgs boson, all unknown parameters of the Standard Model are measured. As the mass of this boson has been measured, the global fit can be carried out including this mass checking the overall consistency [5]. This fit yields a p-value of.7 for the compatibility of all available measurements with the Standard Model. With this global fit, the consistency of the measurements of the W-boson and topquark masses can be checked compared to all other available measurements. This is shown in Figure.6. The electroweak fit is repeated two times. The first fit excludes the measurement of the W-boson mass, the top-quark mass and the BEH boson mass (grey band). Then the fit is rerun including the BEH boson mass (blue band). Comparing the two bands shows clearly that the inclusion of the BEH boson mass improved the predictions significantly. The direct measurement (black marker) shows reasonable agreement with the indirect prediction but it is clear that one can still improve this consistency check with a more precise measurement of both the top quark and W boson

24 6 CHAPTER : The top quark sector of the Standard Model mass. [GeV] M W % and 95% CL fit contours w/o M W and m t measurements 68% and 95% CL fit contours w/o M W, m and M H measurements t M W world average ± σ mkin t Tevatron average ± σ M H =5 GeV M H =25.7 M H =3 GeV M H =6 GeV Figure.6: Global Standard Model fit to electroweak precision data to check the consistency of the measured W-boson and top-quark masses with all other measurements [5] m t [GeV].2.4 The top quark as a calibration tool The top quark is interesting as it allows to further explore the Standard Model as was shown in the previous section. Next to that, the top quark exhibits some interesting properties that can help in calibrating the reconstructed object in the experiment. Large clean samples of top quark pair events can be constructed. These large statistics samples can be used to infer corrections to detector and reconstruction effects. Since the top quark contains a b quark in its decay, one of the potential areas where top quarks can play a crucial role in the performance measurement of the identification algorithms for b quarks in the experiments, or so-called b-tagging [, 2]. This is one of the key topics of this thesis as Chapters 5 and 6 provide a detailed discussion on a method to measure the full b-tagging performance using t t events.

25 Chapter 2 The Large Hadron Collider and the CMS experiment In the previous Chapter, the Standard Model was introduced along with its shortcomings. Theories extending the Standard Model have been developed, but to ultimately prove their validity, they have to be confirmed by experiment. For this reason, high energy particle colliders were built. The Large Hadron Collider (LHC) [5] is currently the largest and most energetic collider in the world giving scientists the tools to pursue a better understanding of the Standard Model and beyond. In Section 2., the Large Hadron Collider will be introduced and some of its main design characteristics will be highlighted. All the experiments located at the LHC are briefly discussed. In Section 2.2 the Compact Muon Solenoid (CMS) experiment [52], playing a crucial role in this thesis, will be discussed in more detail and its main components will be outlined. To finish, a brief overview of the trigger system and computing infrastructure is given. 2. The Large Hadron Collider The Large Hadron collider is currently the most energetic particle collider in the world. It is designed to accelerate proton beams up to 7 TeV and steer them around its 26.7 km ring and force them to collide. The 4 TeV collisions the LHC can generate put it at the energy frontier as they are 7 times more energetic than the proton-anti-proton collisions at.96 TeV provided by the Tevatron collider [53]. The LHC collider has been constructed by the CERN laboratory (European Organization for Nuclear Research) near Geneva, Switserland. The 26.7 km tunnel, home to the LHC, was excavated in the 98 s to install the Large Electron Position collider (LEP). After the shutdown of LEP in 2, construction for the LHC began in the same tunnel and after a commissioning phase in 29, the collider came in operation in March 2 with the first ever 7 TeV centre-of-mass energy collisions at colliders. 7

26 8 CHAPTER 2: The Large Hadron Collider and the CMS experiment 2.. Design of the collider The design of the LHC machine is mainly determined by two factors: the physics reach and the constraints of reusing the old LEP tunnel. Since the physics goals requires to probe the TeV energy scale, the collider needs to produce collisions with sufficient centre-of-mass energy. Since the LHC increased the collision energy by a factor of 7 with respect to the Tevatron p p collider, it is very suitable to probe this energy scale. Another important accelerator parameter defining the physics potential is the luminosity. The luminosity, L, is important because it defines the number of events we can observe for any given process. The number of events for a given process, N, is defined as N = Lσ, (2.) where σ is the cross-section for the given process. Consequently, to search for very rare phenomena, phenomena with a very small cross-section, the luminosity needs to be maximised to be able to observe as many of those events as possible. At the LHC, a luminosity of 34 cm 2 s will be attained at a beam energy of 7 TeV which is roughly times larger than the luminosity of the Tevatron. This provides a large physics potential for the LHC. The decision to build the LHC in the tunnel excavated for its predecessor was mainly made for budgetary purposes. Hence the LHC had to be designed to suit its physics requirements as well as cope with the dimensions of the LEP tunnel. Compared to the leptons at LEP, the LHC protons carry 7 times more energy. Since electrons loose a fraction E of their energy each orbit through synchrotron radiation, defined in eq. (2.2), the beams have a stringent upper limit on their energy. E E4 Rm 4 (2.2) In eq. (2.2) the radius of the accelerator ring is denoted as R, the particle mass as m and the beam energy as E. It is apparent that for a factor 7 increase in particle energy, the accelerator radius should increase by 7 4 which is impossible. On the contrary, the increase in energy can be buffered by the choice of beam particle. The best candidate was the proton since its mass is roughly 2 times larger than the electron mass hence reducing E by a factor of /2 4 compared to an electron accelerator. The most practical choice for a hadron collider would be to collide protons with anti-protons, similar to the Tevatron, where the counter-clockwise rotating beams could be steered by the same magnet system. Unfortunately, the design luminosity at the LHC requires the beam to consist of proton bunches containing up to protons each which is beyond the reach of any anti-proton production system. Hence, the machine was built to collide two counter-rotating proton beams. The difficulty of having two counter-rotating beams with particles of the same charge is that they need two opposite magnetic fields to be guided along the accelerator. Since the LEP tunnel was not wide enough to host two separate accelerators, one per beam, a special twin-bore magnet system was designed to generate the dipole field necessary to steer the beams. The cross section of such superconducting dipole magnet is shown in Figure 2. where two coils are integrated in one cryostat. To steer the

27 CHAPTER 2: The Large Hadron Collider and the CMS experiment 9 Figure 2.: The cross section of a superconducting LHC dipole 7 TeV proton beams around the LHC, a magnetic field of 8.33 T is required. Such high magnetic field can only be produced using superconducting coils operating at a temperature near.9k. The LHC consists of 232 of these 5m long dipole magnets weighing over 27 tons each. In addition to the dipole magnets, a number of higher order fields are used near the interaction points to focus the beam before entering collision. The squeezing of the beams before colliding them helps in attaining the high luminosity required. Before the proton beams can be injected into the LHC machine, they need to have an initial energy of 45 GeV. This pre-acceleration is performed by multiple particle accelerators in the CERN accelerator complex (Figure 2.2). First, protons are collected by stripping the electrons from hydrogen atoms. Then, the protons enter the first accelerator in the chain which is the LINAC2, a linear accelerator. This machine accelerates the protons to an energy of 5 MeV after which they are injected in the BOOSTER. The latter stacks up four accelerators where the protons are squeezed into bunches and further accelerated to.4 GeV. Then the proton bunches enter the Proton Synchrotron (PS) where the beam get s its bunch structure where every bunch is spaced by 25 ns from the previous. The protons also get accelerated to 26 GeV. Finally, the acceleration to 45 GeV is performed by the 6km long Super Proton Synchrotron and the bunches are ultimately injected into the LHC. When filling the LHC machine, 288 bunches can be injected spaced by 25 ns. When the bunches are circulating in the machine, the injection is halted and the acceleration of the beam starts. When the beam reaches its design energy of 7 TeV, it is squeezed and adjusted to have the most optimal conditions for colliding the beams in the interaction points. The beam will typically remain in the machine to provide collisions for the next 5 hours. When the luminosity of the beams is to degraded, the decision is made to dump them and refill the machine afterwards.

28 2 CHAPTER 2: The Large Hadron Collider and the CMS experiment Figure 2.2: The injection chain of the LHC accelerator complex The experiments at the LHC Along the Large Hadron Collider, four interaction regions have been implemented. In these interaction regions, the curved shape of the accelerator is changed to a straight section where the protons of both beams are put on a collision course. Around the four interaction points, large particle detectors have been constructed as shown in Figure 2.3. Figure 2.3: Schematic overview of the LHC accelerator and the location of the four main experiments Two very big general purpose experiments are installed at the Large Hadron Collider, the CMS [52] and the ATLAS [54] experiments. These experiments are often denoted as general purpose experiments since their physics programme is very wide. These detectors are designed to be usable for both the search for new phenomena be-

29 CHAPTER 2: The Large Hadron Collider and the CMS experiment 2 yond the Standard Model as well as to conduct very precise measurements on already known particles such as the top quark. Additional to these very huge general purpose detectors, two smaller and very specific experiments were installed. The first is the ALICE experiment [55]. This experiment mainly focuses on the study of the quark-gluon plasma through analysis of heavy-ion collisions that are delivered by the LHC inbetween proton run-periods. The second is the LHCb experiment [56] which is designed to perform precision measurements in the b-quark sector. Next to the four experiments installed around the interaction points, a detector to measure the total proton-proton cross section and elastic proton scattering is deployed. This detector is named TOTEM [57] and is installed close to the CMS interaction region. Finally, the LHCf experiment [58] measures the particles created in the very forward region of the proton-proton collisions attempting to improve the understanding of ultra-high energetic cosmic rays The LHC run periods The first collisions at 7 TeV centre-of-mass measurement were delivered by the LHC in March 2 after a long commissioning period starting from September 28 when a technical failure in the accelerator severely damaged a number of magnets. During the 2 run, the LHC produced a data sample of 45 pb with a peak luminosity of around 2 32 cm 2 s. Although the peak luminosity is a factor 5 smaller than the design specification, the collisions were the most energetic ever opening the energy frontier at the LHC. Figure 2.4: Integrated luminosity and peak luminosity as a function of time during the 2 operation of the LHC at s = 7 TeV [59]. During the first long run in 2, the machine provided 7 TeV centre-of-mass energy at a peak luminosity of 4 33 cm 2 s as shown in the right canvas of Figure 2.4.

30 22 CHAPTER 2: The Large Hadron Collider and the CMS experiment This provided a total integrated luminosity delivered to the experiments of 6.36 fb which is O( 2 ) larger than during the 2 run. Also the peak luminosity increased by a factor 2. This was up to that point in time the highest reached peak luminosity for a particle collider. In 22, the LHC beam energy was increased from 3.5 TeV per beam to 4 TeV resulting in 8 TeV centre-of-mass collisions. Continuing to build on the successful 2 run, the peak luminosity delivered to the experiments increased again by a factor of almost 2 with respect to the 2 run to little under 8 33 cm 2 s which comes very close to the design luminosity. During this run period, the LHC delivered a dataset of fb proton-proton collisions at 8 TeV as can be seen from Figure 2.5. Currently, the LHC is going through its first 2-year shutdown period gearing up for 3 TeV operation in 25. Figure 2.5: Integrated luminosity and peak luminosity as a function of time during the 22 operation of the LHC at s = 8 TeV [59]. The data sample generated during the 2 and 22 runs will be studied in this thesis. Due to the high luminosity and the large number of protons in each bunch, additional interactions can appear in the experiment next to the central hard interaction, called pileup interactions. The average number of proton-proton interactions per bunch crossing averages to 2 [6] as shown in Figure 2.6 where the distribution of the number of interactions per bunch crossing is shown. In this high-pileup environment it is difficult to determine which particle comes from which pp collision. 2.2 The Compact Muon Solenoid experiment The Compact Muon Solenoid experiment (CMS) is one of the four main experiments reconstructing the proton-proton collisions delivered by the Large Hadron Collider. Additionally, it is one of the two very large general purpose experiments. Together with the ATLAS experiment, its target is further scrutinizing the Standard Model by doing

31 CHAPTER 2: The Large Hadron Collider and the CMS experiment 23 CMS Average Pileup, pp, 22, p s = 8 TeV Recorded Luminosity (pb /.4) <¹> = Mean number of interactions per crossing Figure 2.6: Distribution of the average number of pp collisions per crossing of the LHC beams during the 22 operation at s = 8 TeV [6]. On average, each beam crossing results in 2 pp collisions. precision measurements but also by searching for new phenomena like SuperSymmetry or the search for the elusive Brout-Englert-Higgs boson. The discovery of a boson very compatible with the latter [2, 3] has been by far one of the largest successes of both CMS and ATLAS but also of the LHC. This section will explain in more detail how the CMS detector was designed and which technologies allow it to carefully reconstruct the collisions. Furthermore, a brief overview will be given of the trigger system that allows CMS to reduce the vast amount of 9 collisions per second to a manageable rate. Finally, the computing infrastructure will be briefly introduced that is used by scientists around the world to analyse the data Overview of the detector systems The CMS experiment was designed according to a traditional multi-layered approach typical to collider experiments as shown in Figure 2.7. The CMS experiment has a cylindrical shape of 5 m diameter and is about 22 m long. Although the compact CMS detector is significantly smaller than the very large ATLAS detector. The weight of the CMS experiment totals to an astonishing 5 thousand tons where ATLAS throws in about 5 thousand tons less. The largest fraction of the weight is located in the iron return yoke which is constructed around the very large superconducting solenoid magnet. The magnet delivers a field of 3.8 T to bend the high energetic particles originating from the collisions to allow their momentum to be measured. Interleaved with the return yoke, muon chambers (cfr. Section 2.2.5) are installed as the most outwards detector. Inside the bore of the magnet, there is room to host inner detector layers. The detector system closest to the beam axis and the collision point is the inner tracking detector (cfr. Section 2.2.3). This high precision detector allows to reconstruct charged particle trajectories as well as to measure their momentum in the magnetic field. Exiting the tracking detector, particles enter into the calorimeter system, explained in

32 24 CHAPTER 2: The Large Hadron Collider and the CMS experiment Figure 2.7: Schematic breakdown of the full CMS detector. Section 2.2.4, where their energy is measured either in the electromagnetic calorimeter for electrons and photons or in the hadronic calorimeter for hadrons. Finally an endcap is installed on both sides of the central cylinder, to ensure an almost 4π coverage The CMS coordinate system To describe a certain location in the detector, a common CMS coordinate system has been put in place. At the origin of this coordinate system sits the interaction point where the collisions take place. The x-axis points from the origin towards the centre of the LHC while the y-axis is chosen to point upwards to the ground surface. Finally, the z-axis is set perpendicular to the x and y-axis to form a right-handed coordinate system. To characterise the location of detector material, and even particles, in the detector the azimuthal angle φ and the polar angle θ and the radial coordinate r are used. The azimuthal angle is defined as the angle between the object and the x-axis in the (x,y) plane and ranges from to 2π. The polar angle is measured from the z-axis and takes values between and π. The polar angle is most often translated into the pseudorapidity given by ( η = ln tan θ ), (2.3) 2 Also for positrons

33 CHAPTER 2: The Large Hadron Collider and the CMS experiment 25 such that differences in pseudorapidity are invariant under Lorentz boosts along the beam direction The tracking detector Charged particle tracks can be reconstructed using the inner tracking detector of CMS. This cylinder shaped detector is installed closest to the collision point and is 5.8m long and 2.6m in diameter. The tracker is immersed in a magnetic field of 3.8T allowing it to accurately measure charged particle momenta through their bending in the magnetic field. The tracking detector consists of two main detector technologies: the pixel detector and the silicon strip detector. Figure 2.8: Schematic overview of the CMS pixel detector. The pixel detector is displayed in Figure 2.8 and sits at a radius of less than cm from the beam axis. The pixel detector consists of three layers of x 5 µm 2 pixel cells that are installed respectively at a radius of 4.4 cm, 7.3 cm and.2 cm. The three layers are complemented by two disks located on both sides of the interaction point at z=34.5 cm and 46.5 cm. These disks have pixel cells extending from a radius of 6 cm to 5 cm from the beam axis. The pixel detector contains a total of 66 million pixel cells allowing for a single hit resolution of 5-2 µm in this high-activity area. Outside the pixel detector, the particle density gets low enough to be able to use a silicon strip detector rather than pixel cells. The silicon strip detector, schematically displayed in Figure 2.9 consists of 9.3 million silicon strip sensors and ranges from 2 to 6 cm in radius. In the central barrel of the detector, the strip tracker is divided into two subsystems. The Tracker Inner Barrel (TIB) consists of 4 layers covering up to z < 65 cm. At each side of the TIB it is complemented with three additional disks, the Tracker Inner Disks (TID). The Tracker Outer Barrel (TOB) is located outside the TIB and consists of six layers of silicon strip detectors in a range of z < 8 cm. On each side of the barrel, nine disks are installed in the region 24 < z < 282 cm at a radius of 22.5 to 3.5 cm. This system is called the Tracker Endcap (TEC). The silicon strip tracker provides coverage up to η < 2.5 and provides a single hit resolution in the TIB of µm on the r φ measurement and 23 µm for the z-direction. For the TOB, the respective single hit resolutions are µm and 53 µm.

34 26 CHAPTER 2: The Large Hadron Collider and the CMS experiment Figure 2.9: Schematic overview of the CMS tracking detector. Track reconstruction In both the pixel and silicon strip detectors, the position of a charged particle traversing the layer is recorded along with its uncertainty. These hits can then be used to reconstruct the actual track of a particle followed while traversing the full tracking detector in the magnetic field. Reconstructing tracks from the tracking detector hits can be done in four steps. First the track seeds are generated. These are then used to build tracks. Possible ambiguities are removed and the final track fit is performed [6]. The seeds are generated from the reconstructed hits in the tracker and the seeds need to consist of at least three hits in the tracker or two hits with a beam constraint. The best seeds are provided by the pixel detector as it has the best position resolution. Nevertheless, inclusion of strip tracker seeds allows for improvement of the overall track reconstruction efficiency. These seeds provide initial trajectory candidates that are now passed to the track builder. The charged particle tracks are reconstructed using a Kahlman filter. The tracks building starts from the initial trajectory candidate provided by the seed generating step and starts to extrapolate them outwards. Compatible hits are identified based on the extrapolation towards each compatible layer using the equations of motion of a charged particle in a magnetic field. The effects of multiple scattering are taken into account in this extrapolation. The compatible hits are added to the trajectory candidates to form a new candidate for which the track fit is repeated. This iterative process is continued until the trajectory candidate is extrapolated to the final layer of the tracking detector. To reduce the collection of trajectory candidates, the trajectories not fulfilling a cut on the normalised χ 2 of their fit are removed as well as tracks with to few associated hits. In the final list of trajectory candidates, two or more trajectories could share tracker hits as well as seeds. These ambiguities have to be removed before the global track fits

35 CHAPTER 2: The Large Hadron Collider and the CMS experiment 27 are performed. To do this, tracks sharing too many hits are discarded from the list only retaining the track with the most hits. Finally, the trajectory candidate list is obtained and all ambiguities are gone. To ensure an optimal determination of the track parameters, the track is refit completely using a least-squares minimisation taking into account all the tracker hits assigned to the track candidate. Initially, the track parameters are propagated outwards from the beam line to the calorimeter surface. Subsequently, the track fit is carried out in the reverse direction starting from the outermost tracker hit. To retrieve the trajectory information at the impact point, the track can be extrapolated from the first layer containing a tracker hit to the interaction region. Vertex reconstruction When all the tracks are reconstructed they can be used to reconstruct the vertex. This reconstruction uses a technique called Deterministic Annealing (DA) [62] to cluster the tracks into a vertex candidate. The method assigns each track to a vertex candidate and then minimises a global χ 2 where the candidates are weighed to account for their compatibility to the tracks. A temperature parameter T is introduced to control the assignment of tracks to vertices. Starting at infinite temperature, all weights are equal and only one vertex candidate is available. Then the temperature gets decreased incrementally where in each step the prototype is split in two. If all tracks are not compatible to one vertex candidate, the process continues potentially further splitting the vertex candidates. The process is continued until a minimum temperature is reached. Vertices with less than two tracks assigned will be removed from the list to remove fake vertices from track outliers. The track list is then fitted again with the Adaptive Vertex Fitter [63] to get the vertex position in three dimensions. This fitter weights all tracks based on their distance to the primary vertex to further reduce the effect of charged particles originating from the decay long-lived particles The calorimeters The CMS calorimeter is built up in two different subsystems. The first, the electromagnetic calorimeter, is a nearly hermetic and homogeneous calorimeter designed to measure the energy for electromagnetically interacting particles. Just outside the electromagnetic calorimeter sits the hadronic calorimeter to measure energy deposits from neutral and charged hadrons. Since these particles can traverse more material, the hadronic calorimeter is designed as a sampling calorimeter interchanging layers of sensitive material with brass to provide the necessary stopping power. Electromagnetic calorimeter The electromagnetic calorimeter (ECAL) of CMS, shown in Figure 2., is a homogeneous detector constructed from lead tungstate (P bw O 4 ) crystals. Due to the relatively short radiation length (X ) of these crystals, the ECAL can stop high energetic electrons while still remaining relatively compact. This is important for fitting this detector into the solenoid bore. Furthermore, 8% of the light is emitted within a 25

36 28 CHAPTER 2: The Large Hadron Collider and the CMS experiment Figure 2.: detector. Detailed view of a quarter of the ECAL calorimeter in the CMS ns time window making it ideal for LHC operation. These properties together with its radiation hardness make the crystals a good choice for the ECAL. The calorimeter is segmented into three parts, the ECAL Barrel (EB), the Endcaps (EE) and the Preshower (ES). The ECAL Barrel detector has an inner radius of 29 cm and contains about 62 crystals. These crystals cover an η range up to.479 and are mounted such that their surface is facing the interaction region though they are tilted by 3 to reduce the effect of particles crossing the boundary in between adjacent crystals. The crystals cover a surface of 22 x 22 mm 2 with a length of 23 mm corresponding to 25.8 radiation lengths. Additionally, both endcaps contain 4648 crystals with a surface size of 28.6 x 28.6 mm 2 and a length of 22 mm. This system extends the ECAL coverage to a pseudorapidity range of.479 < η < 3.. The last part of the ECAL is the Preshower detector located in front of the endcaps in the region.653 < η < 2.6. This detector consists of lead radiators to initiate electromagnetic cascades interleaved with silicon sensors of 63 x 63 mm 2. This detector allows to identify neutral pions in the endcaps and helps improving the identification and position resolution of electrons in the endcaps using its high granularity. The ECAL provides an energy resolution (σ E /E) of -2% for η <. increasing to 4% when going up in pseudorapidity [64]. Hadronic calorimeter The hadronic calorimeter (HCAL) is designed to measure the energy of hadrons and it plays a crucial role in the measurement of the missing transverse energy. The latter is the energy that is attributed to very weakly interacting particles such as neutrinos 2. Unlike the ECAL, the HCAL is a sampling calorimeter consisting of around 7 plastic scintillator surfaces combined with layers of brass absorbers. The HCAL Barrel (HB) has to fit inbetween the ECAL and the magnet. Since that does not leave much room for the HCAL, as much absorbing power needs to be positioned inside the magnet region reducing the space for sensitive detector material. The HB covers a pseudorapidity range up to η <.3 with calorimeter towers of.87 x.87 in (η, φ) coordinates. The segmentation of the HCAL is shown in Figure The concept of missing transverse energy will be further discusses in the next chapter.

37 CHAPTER 2: The Large Hadron Collider and the CMS experiment 29 Figure 2.: detector. Detailed view of a quarter of the HCAL calorimeter in the CMS Given the limited space for the HCAL inside the magnet coil, hadronic shower leakage can occur. As a consequence, an extra layer is added just outside the magnet called the HCAL Outer detector (HO). This system covers.26 < η <.26 and uses the same segmentation of HB, albeit with iron absorbers instead of brass. The HCAL Endcaps (HE) on both sides of the barrel have a range.3 < η < 3. partially overlapping with the barrel detector. The tower size in HE is the same as for HB up to η <.74. Beyond this region, the tower sizes are incrementally enlarged to a maximal size η φ size of Finally, this system is complemented with a forward hadron calorimeter (HF) inserted at.2 m from the interaction region along the z-axis. This calorimeter allows to measure hadronic activity in the very forward region upgrading the HCAL coverage to η < 5.. The resolution of the HCAL system was determined in a test-beam with single pions crossing the prototype detector [6]. The single-pion resolution for ECAL+HB was found to be 2-3% below 5 GeV improving to less than % for 3 GeV particles The muon system The muon system is the outer most subdetector of CMS. The muon system ensures a very precise reconstruction of the muons complementing the inner tracker and the calorimeter. The layout of a slice of the system is provided in Figure 2.2 where it can be seen that the system comprises of three different detector technologies. The choice of the detector technologies is mainly determined by the different operating environments in the detector. In the barrel region up to η <.2, the muon detection layers are interleaved with the iron return yoke responsible for closing the magnetic field lines of the solenoid. Hence, the residual magnetic field at the position of the muon chambers is small. Combined with a low muon flux this far out from the beam axis, Drift Tubes (DT) can be used. These DTs have a very good single-hit spatial resolution of around µm and an angular resolution of mrad. Conversely, the magnetic field and muon flux in the forward region are larger.

38 3 CHAPTER 2: The Large Hadron Collider and the CMS experiment Figure 2.2: Longitudinal view of a slice of the CMS muon system showing the three different detection technologies used and their coverage. Hence, Cathode Strip Chambers (CSC) are used in the endcaps covering a pseudorapidity ( η ) range of.9 to 2.4. These chambers also exhibit a good single-hit position resolution of typically 2 µm with an angular resolution of the order of mrad. Both CSCs and DTs are accompanied by Resistive Plate Chambers (RPC). These detectors are very fast and provide a very good time resolution of the order of ns albeit with a more crude position resolution. The function of the RPCs is mainly to trigger on muons as well as to determine the correct bunch crossing in which the muon was produced. The first two barrel layers of the DT system are sandwiched between two layers of RPCs while the other DT layers have one accompanying RPC layer. The RPCs accompany the CSCs in the endcaps as well but only up to η < The trigger system During nominal operation at design luminosity the LHC will deliver up to 9 inelastic collisions per second. With an average single event size of the order of MB, it is clear that no storage system available to date can cope with such high rate of incoming data let alone store it. Therefore a trigger system needs to be implemented taking a decision on each event to be stored on tape. The decision is made in two steps. The first selection is made by the very fast Level trigger. Events passing this step are fed to the High Level Trigger that makes the final call. Level trigger (L) As the LHC delivers collisions every 25 ns, a trigger decision has to be made at this rate. Since this time frame is very short to make a full reconstruction of the detector, a specialised electronics trigger was installed in the Underground Service Cavern (USC) adjacent to the experimental hall. Since 25 ns is very short even for specialised elec-

39 CHAPTER 2: The Large Hadron Collider and the CMS experiment 3 tronics, a buffer memory is installed next to the detector to host 28 collisions. This leaves the L trigger just over 3 µs to make a decision for a particular event. Albeit that about 2 µs are already used for the transportation of the information to and from the trigger system. To cope with this short timescale, the L trigger uses very fast algorithms to make a decision based on crude information from the muon stations and the calorimeters. The L trigger has a maximal output of khz. High Level Trigger (HLT) Once the events passed the L trigger, they are shipped to the surface buildings where the High Level Trigger farm (HLT) is located. Since the event rate dropped by a factor 4 thanks to the L trigger, it is now possible to work with commercial CPUs as the decision time window is now of the order of seconds. To decide if an event should be kept and stored on tape, the HLT has access to the fully reconstructed event and uses complex algorithms, similar to the ones used in offline analysis, to make the decision The LHC computing grid To make all the collected data available to scientists worldwide, the LHC has a special distributed computing system: the Worldwide Large Hadron Collider GRID (WLCG) [65]. This system foresees both massive storage capacity throughout the world but also the necessary computing power to process all the data and simulation. The WLCG groups together GRID systems from smaller geographical areas like the EGEE (Europe) and the OSG (United states). The GRID consists of a hierarchical tiered structure. Tier- The Tier- centre is located at the CERN Meyrin site and is the place where all the LHC experiments sent their data to. The data from CMS arrives here from the HLT and the prompt reconstruction is carried out. The Tier- centre permanently stores this data and is continuously used for very high priority workflows such as detector calibration. Tier The Tier centres are scattered across Europe, the USA and Asia. In total CMS is attached to about 6 of these centres. The Tier centres receive the data from the Tier- centre at CERN such that for each dataset more than one copy exists on the GRID at all times. The Tiers then distribute the data further downstream to the Tier-2 sites connected to them. Sometimes analysis jobs are run on these sites whenever they require very high priority. These GRID sites are also responsible for staging the simulated samples as well as running re-reconstruction of the data whenever needed.

40 32 CHAPTER 2: The Large Hadron Collider and the CMS experiment Tier-2 The Tier-2 GRID sites are those that are used for the data analysis. These clusters are usually smaller in size yet contain some significant storage capabilities. They receive data and simulation samples from the Tier centres to provide access to the physics community. These sites are also used to generate simulation samples. The benefit of this structure is that the data and simulation is at all times stored on different sites across the world. This provides scientists easy access to the data they want to analyse since the system allows to submit analysis jobs to a central Workload Management System (WMS). The WMS matches the job to a given GRID site based on the required input dataset and the available resources at sites hosting the required sample. This makes analysis for the user particularly simple as he or she does not have to know where the data or simulation is hosted, nor has to transfer the data to local machines. One of the Tier-2 centres is hosted in Brussels at the VUB/ULB computing centre. This Tier-2 site provides 8 job slots and about.2 petabyte of storage capabilities. This cluster allows both local collaborators to carry out their analysis as well as providing access to the wider community to the samples hosted here CMS Data taking during the 2 and 22 LHC runs Data taking efficiency Figure 2.3: Integrated luminosity as a function of time during the 2 and 22 proton-proton running of the LHC at s = 7 and 8 TeV [66]. The luminosity delivered by the LHC is compared to the recorded luminosity by CMS. The validated luminosity depicts the data that is certified for physics analysis. When the LHC machine is filled with two counter rotating proton beams and they are set to collide, the LHC experiments start recording the collisions. It is clear from the previous that an experiment like the CMS detector is very complex. Hence, recording data with the CMS detector does not happen by flipping the on/off -switch. Conversely, operating the CMS experiment requires a 5-person shift crew to continuously

41 CHAPTER 2: The Large Hadron Collider and the CMS experiment 33 steer and monitor the apparatus around the clock. In the control room, a person is in charge of the data acquisition (DAQ) system accompanied by another person that monitors the trigger. Furthermore, the integrity of the data is checked by a Data Quality Monitoring shifter and finally the operation is overseen by the shift leader. Last but not least, the Detector Control System shifter is assigned to oversee the hardware from cooling to high-voltage power and needs to respond quickly in the event of failure of any system. Even with this continuous monitoring of the experiment, it sometimes happens that while the LHC is providing collisions, CMS is unable to record them. This could happen because the run is stopped by a malfunction of one of the subdetectors. The data recording is then resumed when the issue is fixed. This means that overall CMS is recording a little less integrated luminosity than the LHC is providing as is shown in Figure 2.3 where the recording efficiency of CMS is 9.5% in 2 and 93.5% during 22 operation. Data certification After the data is recorded by the CMS experiment, it immediately gets partially reconstructed for the Data Quality Monitoring (DQM) system. Each run recorded by the CMS experiment gets certified both online, i.e. during data-taking, and offline, i.e. after data-taking. For physics analyses, there are certain requirements on the data: the tracking detector should be operational as well as the calorimeters and the muon system. For this purpose, the data has to be certified before physicists can analyse it. The certification is done by the Data Quality Monitoring shifters that look for anomalies in the detector response during data taking. These anomalies can be any range of things from a sub-detector being switched off or in the wrong operating mode to certain modules producing too much noise or malfunctioning. A typical distribution from the tracker certification is shown in Figure 2.4. The plot shows the occupancy map of the pixel detector which is used to look for any holes in the detector. These holes are areas in the detector that do not function properly and hence are not producing tracker hits. The occupancy map for each run is then cross-checked to previous runs to assess if new holes have appeared. Finally, when the certification is over, a list of all certified runs is propagated to all analysts. This list can then be used in analysis to select only the data that is found to be adequate to produce physics results where the detector is found to be operating well. This kind of certification file is used in the analyses presented in this thesis.

42 34 CHAPTER 2: The Large Hadron Collider and the CMS experiment Figure 2.4: A typical distribution from the tracker detector Data Quality Monitoring system. The pixel detector occupancy is shown as a function of the (z,φ) position in the detector. This map allows to spot white areas, called holes, where the pixel modules are not working properly.